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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
|Verification status (*):||PRP|
|Official Comment:||Partitions, ECPP|
|Proof-code(s): (*):||c46 : Boncompagni, Primo|
|Decimal Digits:||6098 (log10 is 6097.2130611034)|
|Rank (*):||68851 (digit rank is 1)|
|Entrance Rank (*):||57378|
|Currently on list? (*):||no|
|Submitted:||3/24/2011 12:01:39 CDT|
|Last modified:||3/26/2011 16:50:54 CDT|
|Blob database id:||250|
|Score (*):||30.9053 (normalized score 0)|
(from blob table id=250)
p(30037918) is the number of partitions of the number 30037918. For the primality proof, see the PRIMO certificate
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 137
(archival tag id 213175, tag last modified 2013-05-18 19:50:29)
- Partitions (archivable *)
- Prime on list: no, rank 24
(archival tag id 213176, tag last modified 2012-12-19 19:20:28)
The Top 5000 Primes is a list for proven primes only. In order to maintain the
integrity of this list, we seek to verify the primality of all submissions.
We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial
divide and PRP
check every entry before it is included in the list.
|machine||RedHat P4 P4|
|notes||PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5]|
Primality testing 1633281727...3864196297 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.10% and helper 0.01% (0.33% proof)
1633281727...3864196297 is Fermat and Lucas PRP! (12.5437s+0.0036s)
[Elapsed time: 13.00 seconds]
Query times: 0.0005 seconds to select prime, 0.0001 seconds to seek comments.